The introduction of X-ray Computed Tomography (CT) in 1972 revolutionized Medical Imaging, replacing classical qualitative imaging by a quantitative format. Mathematics has since played a crucial role in several aspects of this vast discipline. While inversion of the Radon Transform was the basic starting point for CT, various other current and emerging imaging modalities (such as MRI, PET, Ultrasound, Elastography, Impedance Imaging, Photoacoustic Imaging, Thermography) each require the solution of different mathematical Inverse Problems to produce images from the corresponding physical measurements. Once images have been obtained, their immensely important current and future clinical use gives rise to a number of Image Analysis problems: segmentation, noise removal, deblurring, registration. Furthermore, in an exciting emerging area, determination of tissue parameters by medical imaging methods is used in Patient Specific Modeling of biological processes, promising to reach a whole new level of diagnostic and therapeutic planning techniques.
All three areas of Medical Imaging identified above (Inverse Problems, Image Analysis and Patient Specific Modeling) have seen significant mathematical developments, involving deep new analytic and geometric tools.
The aim of the workshop on "Analytic and Geometric Methods in Medical Imaging" is to establish connections between recent analytic and geometric work in Inverse Problems and analytic and geometric methods being developed by researchers in Image Processing and Patient Specific Modeling.